Proof of claim REF .
Note that \((Q_t^{q,\gamma })_{t \ge 0}\)  is a continuous local martingale since it is a stochastic integral of a progressively measurable process with respect to Brownian motion [1]}.
Since \(Q_t^{q,\gamma } \in [0,1]\)  for any \(t \in [0, \infty )\)  by the definition of \(\Gamma (q)\) , it is a bounded local martingale, which is indeed a martingale [1]}.
